For Sigmund Freud, it was anatomy. For Neil LaBute, destiny has always been about looks. Good looks, especially in men, mean that you’re a privileged, caddish user. How appropriate then that LaBute’s adaptation of August Strindberg’s “Miss Julie,” being given its world premiere at the Geffen, should find helmer Jo Bonney casting an actor with male-model good looks to be John, the rough upstart servant who attempts to switch roles with the heiress Julie. It’s inspired miscasting.

Or is putting Logan Marshall-Green together with Lily Rabe merely casting against type, and adding texture to an already multi-level battle of the sexes and classes? Frankly, Marshall-Green’s features are finer than Rabe’s. Also, his clear tenor is placed slightly higher than her raspy contralto. And when she snorts with laughter or burps after drinking too much wine, we believe Rabe. We don’t quite buy Marshall-Green when he sucks his teeth or drops a consonant at the end of a phrase.

A few minutes into this “Miss Julie,” you might think that the Geffen Playhouse started out with a traditionally cast “The Heiress” and then switched plays after losing a few key supporting players. Julie’s fall at the hands of this John isn’t so devastating. But the injustice of her money and his lack of it is more pronounced.

To drop yet another title into this review, the casting in James Cameron’s “Titanic” had a similar leveling effect. Leonardo DiCaprio looks to the manner born once he dons a tuxedo, while it’s Kate Winslet who looks more at home dancing with the masses in steerage.

Just in time for yet another movie adaptation of “The Great Gatsby,” Bonney and LaBute update Strindberg’s 1888 classic to 1929 and move it to a Long Island estate, adding a “bitch” here and a “shit” there.

As much as this Julie and John go at each other, they’re never the ones in control. Julie’s offstage father pulls the purse strings and John’s servant-girlfriend (Laura Heisler) is pregnant and speaks with a Yiddish flair despite calling herself Kristine.

Maybe looks aren’t what they’re cracked up to be after all.

Miss Julie

(Audrey Skirball Kenis Theater, Los Angeles; 117 seats; $99 top)

A Geffen Playhouse presentation of a play in one act by August Strindberg, adapted by Neil LaBute. Directed by Jo Bonney. Set, Myung Hee Cho; costumes, Christina Haatainen Jones; lighting, Lap Chi Chu; sound, Vincent Olivieri. Opened and reviewed May 1, 2013. Running time: 1 HOUR, 40 MIN.

With: Lily Rabe, Logan Marshall-Green, Laura Heisler